Probabilistic Message-Passing Control

There is insufficient current understanding of how to apply fully decentralized control to networks of sparsely coupled nonlinear dynamical subsystems subject to noise to track a desired state. As exemplars, this class of problem is motivated by practical requirements of creating decentralized power grids robust to cascade failures, the digital transformation of Industry 4.0 managing IoT connectivity reliably, and controlling transport flow in smart cities by computing at the edge. We demonstrate that an approach utilizing probability theory to characterize and exploit the uncertainty in locally received information, and locally optimized messages passed between neighboring subsystems is sufficient to implicitly infer global knowledge. Thus, control of a global state could be realized through decentralized control signals applied only to local subsystems using only local information without any reference to a global current state. Given a global system that can be decomposed into a set of locally coupled subsystems, we develop a theoretical method of probabilistic message passing and probabilistic control signals all interacting only at the subsystem level, but which promotes a system-wide convergence to a desired state. Our theoretical results are corroborated using computational experiments on a network of a 10-node partially coupled system decomposed into four separated subsystems with control inputs applied and determined at the subsystem level. Comparing the results with a centralized control method utilizing information from all the nodes to achieve global state convergence validates our hypothesis that local decentralized probabilistic control can be affected by the mechanism of local probabilistic message passing without needing access to global centralized information. We also provide a set of numerical experiments increasing the network size showing that the decentralized algorithm is independent of the global system size.